The β-barrel Assembly Machinery Complex

Outer membrane proteins (OMPs) of Gram-negative bacteria are synthesized in the cytoplasm and transported across the inner membrane by SecYEG translocon into the periplasm. The survival factor A (SurA) chaperones carry the unfolded membrane proteins across the periplasm to the BAM complex, which is responsible for the insertion and assembly of OMPs into the outer membrane [1].

In E. coli BAM complex consists of a membrane protein BamA and four lipoprotein subunits BamBCDE. These subunits associate with BamA through periplasmic POTRA domains. In vitro reconstitution of the E. coli BAM complex and functional assays showed that all five subunits are required to achieve the maximum activity of BAM [1].

In theory, recruiting the BAM complex in a cell-free system could be extremely beneficial as it could integrate OmpA and lgA protease beta-domain into the membranes of liposomes from the inside without requiring any additional protein complexes. Also, this would make a cell-free system more ubiquitous, because BAM complex does not require any signal sequence for proper protein insertion. In order to ensure quick integration, BamA needs to be consistently present at high yields throughout the expression of OmpA and lgA. For this reason, it is essential to stimulate its expression by an initial addition of mRNA, ensuring rapid expression of BamA. For this reason, with the help of Edinburgh iGEM team (special thanks to Freddie Starkey), a mathematical model for BamA kinetics was created.

Mass Action Equations

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First of all, to represent chemical reactions and to render a start for mechanistic modelling, Mass Action Equations were used. It is known that the laws of mass action state that the rate of a chemical reaction is directly proportional to the product of the activities or concentrations of the reactants. The mass action equations in Figure 1 can be used to represent basic protein expression:

Fig. 1

Fig. 1 Mass Action Equations for Protein Expression

Each of these equations is used in triplicate to represent the expression of BamA, OmpA and lgA respectively and from these mass action equations a system of ordinary differential equations can be derived.

Ordinary Differential Equations

The model uses a set of differential equations:

Fig. 2

Fig. 2 System of differential equations for BamA kinetics

Determination of the System Values

In order to solve this system it is first necessary to derive values for all the parameters used:

1. copies_BamA, copies_OmpA, copies_IgA - Relative number of plasmid copies.

It is important to consider the effect of different starting masses of DNA of BamA, OmpA, and lgA, therefore to calculate the number of plasmids from which each protein can be expressed. Assuming that we add 25-1000 ng of DNA to our system [1], a single base pair has mass of 650 Da, and the length of each plasmid is known, mass of each plasmid was calculated:

1. peT2Ab with BamA - 5089.5 kDa
2. pRSETb with OmpA - 2550.95 kDa
3. pRSETb with lgA - 2490.8 kDa

Knowledge that 1 ng equals to 6.022∗1017 kDa, allows to calculate the number of plasmids present for a particular number of ng of DNA added (Tab. 1).

Tab. 1 Number of plasmids present for a particular number of ng of DNA added

peT2AB with BamA
DNA added (ng)	Number of copies
25	2.985*1015
250	2.958*1016
1000	1.183*1017
pRSETb with OmpA
DNA added (ng)	Number of copies
25	5.902*1015
250	5.902*1016
1000	2.361*1017
pRSETb with IgA>
DNA added (ng)	Number of copies
25	6.04415
250	6.04416
1000	2.41817

2. tr_BamA, tr_OmpA, tr_IgA - Transcription rate.

Transcription rate of T7 RNA polymerase is approximately 60 nucleotides per second [2]. Length of each gene was 2430 nucleotides for BamA, 1038 nucleotides for OmpA, and 945 nucleotides for lgA. Transcription rate per minute for each gene was calculated:

1. tr_BamA = (60/2430)∗60 = 1.48 mRNAs per minute
2. tr_OmpA = (60/1038)∗60 = 3.47 mRNAs per minute
3. tr_lgA = (60/945)∗60 = 3.81 mRNAs per minute

3. deg_{mRNA BamA}, deg_{mRNA OmpA}, deg_{mRNA IgA} - mRNA degradation rate.

Degradation rate is calculable from half-life using the formula: degX = ln(2)/halflife [3], where X shows the transcript of the target gene. Average mRNA half-life approximately is 5 minutes, however we screened half-lives of 1, 5, 10, and 15 minutes for each protein in order to more precisely evaluate the variability of the results. Degradation rates per minute were calculated:

1. 1 minute half-life - 0.69 mRNAs per minute
2. 5 minute half-life - 0.14 mRNAs per minute
3. 10 minute half-life - 0.07 mRNAs per minute
4. 15 minute half-life - 0.05 mRNAs per minute

4. trl_BamA, trl_OmpA, trl_IgA - Protein translation rate.

Translation rate is about 20 amino acids per second [2]. Lengths of target proteins are 2430 nucleotides for BamA, 1038 nucleotides for OmpA, and 945 nucleotides for lgA. Translation rates per minute were calculated:

1. trl_BamA = (20/810)∗60 = 1.48 proteins per minute
2. trl_OmpA = (20/346)∗60 = 3.47 proteins per minute
3. trl_lgA = (20/315)∗60 = 3.81 proteins per minute

5. deg_BamA, deg_OmpA, deg_IgA - Protein degradation rate.

Protein half-life was determined using ProtParam Tool, which uses the N-end rule [4] to determine protein half-life. The estimates given for each of BamA, OmpA, and lgA are >10 hrs in E. coli. In order to reflect the inexact nature of these computationally derived half-lives, we screened over possible half-lives of 10, 20, and 30 hours for each of BamA, OmpA, and lgA. Applying prior used degradation rate formula degX = ln(2)/halflife [3], this yielded degradation rates per minute of:

1. 10 hour half-life - 1.16∗10⁻³ proteins per minute
2. 20 hour half-life - 5.78∗10⁻⁴ proteins per minute
3. 30 hour half-life - 3.85∗10⁻⁴ proteins per minute

Starting Conditions

In order to examine the effects of higher initial mass of BamA RNA, 6 different values were screened over (Tab. 2). Assuming that addition of RNA in IVTT system is between 1 and 5 µg, the masses of sense and antisense strands of BamA in kDa [6] are 830.382 and 820.8, respectively, and conversion is 1 µg = 6.022∗10²⁰ kDa, the number of RNA molecules added can be calculated using the formula µgadded∗(6.022∗10²⁰/((830.382+820.8)/2)).

Tab. 2 Initial BamA mRNA

RNA added (µg)	RNA added (molecules)
0	0
1	7.29*1017
2	1.46*1018
3	2.19*1018
4	2.92*10
5	3.65*1018

The primary aim of this model was to identify parameters leading to rapidly-achieved and consistently high levels of BamA under conditions of co-expression of BamA, OmpA, and lgA. Prior to this it was important to identify particular parameters leading to these conditions and to examine some general trends. The number of molecules of mRNA and protein for each average, minimum and maximum plot and each of BamA, OmpA, and lgA after 2 hours were calculated (Fig. 3) and summarized (Tab. 3).

Fig. 3.1 Fig. 3.2

Fig. 3Minimum, maximum and average levels of mRNAs and protein for BamA, OmpA and lgA

Tab. 3Average, minimum and maximum number of protein molecules after 2 hours' Protein Number of molecules Average/td> BamA 2.8*10²⁰ OmpA 2.78*10²¹ IgA 3.44*10²¹ Minimum> BamA 1.95*10¹⁸ OmpA 2.13*10¹⁹ IgA 2.63*10¹⁹ Maximum> BamA 1.28*10²¹ OmpA 1.28*10²² IgA 1.58*10²²

In average, minimum, and maximum cases the protein expression of OmpA, lgA, and BamA follows the same trend which is unaffected by fluctuations of mRNA level. Each protein is expressed at a rate primarily proportional to its length and to a magnitude primarily dependent on the mass of available DNA.

Sensitivity Analysis

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Fourier Amplitude Sensitivity Testing (FAST) indices represent the proportion of the output variance of the model attributable to a particular variable and its interactions. Focusing on BamA expression as the protein of interest, total order FAST sensitivity indices were calculated using the BamA protein level each 20 minutes as the model output (Fig. 4).

Fig. 4

Fig. 4 FAST sensitivity analysis of BamA

As it can be seen from the graph, number of BamA plasmid copies contributes most to output variance over the whole time span. Also, BamA mRNA degradation rate is considerably faster than BamA degradation rate - with mRNA halflife of the order of minutes and protein halflife of the order of hours - hence the greater FAST index.

Conclusions

Prior to starting the wet lab experiments, we had hypothesized that the addition of mRNA into our system would ensure that BamA folded and inserted into liposome membrane more efficiently, thus enhancing the expression of OmpA and IgA. Therefore it was decided to purify BamA mRNA and add it to the reaction mixture as a template instead of DNA as we assumed that skipping the transcription step would increase protein synthesis rate. After creating a mathematical model that calculated the necessity of mRNA addition to IVTT system, we were able to generate a more efficient transcription-translation system in which we used both the purified BamA mRNA and DNA. This model clearly revealed that using both mRNA and plasmid DNA in our system was essential as BamA mRNA did increase the rate of protein expression while this effect was proportional to the mass of initial DNA. However, after experimenting in the wet lab, we chose to use purified BamA as it was desired to reach higher expression yields of membrane proteins and it proved to be more effective as BamA mRNA degradation rate was considerably faster than BamA protein degradation rate.

References

1. Gu, Y. et al. Structural basis of outer membrane protein insertion by the BAM complex. Nature 531, 64-69 (2016).
2. Biolabs, N. PURExpress® In Vitro Protein Synthesis Kit | NEB. International.neb.com (2018). at < https://international.neb.com/
3. Philips, R. What is faster, transcription or translation?. Book.bionumbers.org (2018). at
4. Exponential decay. En.wikipedia.org (2018). Accession: at
5. Bachmair, A., Finley, D. & Varshavsky, A. In vivo half-life of a protein is a function of its amino-terminal residue. Science 234, 179-186 (1986).
6. RNA Molecular Weight Calculator | AAT Bioquest. Aatbio.com (2018). Accession: at

Background

eXplaY logo

During the past several decades, display systems have been successfully implemented in linking the genotype to phenotype of particular proteins. While some of these systems naturally occur in nature, some are artificially created in laboratory. Overall, the display systems have been widely used for protein research. For a brief overview of these systems, BBa_K2622029 click here.

One of the nearest future applications of SynDrop is liposome surface display. It stands out from the other display methods as it has fully controllable settings of an experiment such as the optimized interior composition for synthesis and adjusted exterior configuration for protein folding. Unlike cells, liposomes are free of unnecessary cross-talk and biological noise. Additionally, high-throughput production of liposomes might reduce the experimental time substantially.

To achieve this goal, we chose a prokaryotic membrane protein - OmpA (Outer membrane protein A) - it was successfully used as a membrane protein which enables the display of a fused globular protein in prokaryotes1. In our case, we wanted to demonstrate two different proteins: scFv with affinity to vaginolysin2 and camelid nanobody, capable to interact with a GFP molecule3 . These membrane proteins were chosen to mimic targets of current display systems.

In nature, OmpA surface display system flips the selective protein from the inside of the living organism to the outside of its’ surface4. By achieving this in liposomes, the bottom-up approach would allow us to understand the mechanism and relevant components of the flipping process. For this reason, we decided to model a simple system with few variables to evaluate the activity of the fusion protein containing OmpA and Anti_GFP - it seemed like a good starting point to investigate well characterized parts. This is where molecular dynamics GROMACS package came in handy. GROMACS is a powerful open-sourced tool to build simulations of protein folding and lipids interactions. With a huge help from iGEM team Groningen molecular thermodynamics model with GROMACS was built.

Setup

Sequence of particular fusion protein was built BBa_K2622029.

Fig 1 Sequence scheme of Lpp_OmpA and Anti_GFP nanobody fusion protein.

Next, the fusion protein was constructed. The sequences of OmpA and anti-GFP (PDB: 3OGO) were joined exactly where they will be fused according to the DNA sequence using PyMOL (Fig. 2). To start, the structure of OmpA (PDB: 1QJP) had to be reconstructed as parts of it are missing in the crystal structure. This was achieved using the “modeler” software, a python module for homology modeling. The same structure was used as the reference structure and so the filled in structure only serves to complete the molecule.

Then the fusion protein was coarse grained by the martinize script, producing a well calibrated coarse grained bead mapping for the fusion protein in the MARTINI 2 forcefield. The fusion protein was then inserted in a DOPC bilayer constructed by the insane.py script.

GFP was also coarse grained using martinize and inserted in the system containing the fusion protein and the DOPC bilayer, after which the system was solvated with regular water beads. 150mM equivalence of NaCl was added to neutralize the system. For both coarse grained structures, an elastic network was applied with a cutoff of 0.5nm such that the beta-barrels of the proteins are maintained.

Fig 2 The molecular system. Left image represents the fused Lpp_OmpA+anti_GFP inserted to a DOPC lipid bilayer while the coarse grained structure of GFP is presented on the right.

To set up a calculation, the system having the simplest and least variables containing configuration was chosen:

1. Lipid membrane, containing DOPC lipids only
2. GFP molecules surrounding the membrane
3. Lpp_OmpA+Anti_GFP (transmembrane protein + globular protein with affinity to GFP)

Common parameters for martini were used for minimization and equilibration, and the model was setup to run for about 10 microseconds with berendsen temperature coupling and Parrinello-Rahman pressure coupling. The system runs at 300 K and a pressure of 1 bar.

The building process is documented on the project’s github page

Results

Binding between anti-GFP and GFP was visualized over time in Fig. 3 to validate that the model functions as expected. Fig. 3 shows that binding occurs after roughly 1 ms and is quite strong as expected.

The Root Mean Square Deviation (RMSD) was computed over time using GROMACS and plotted in Fig. 4 to show OmpA unfolding over time. The entire event takes place over a time scale of roughly 1 ms.

Due to a strong tendency to shield charged residues within the remaining barrel structure from interacting with apolar lipids tails, a part of the transmembrane OmpA stays anchored in the lipid bilayer Fig. 5. The figure shows clearly that red and blue (charged) side chains are kept within the remnants of the beta barrel and only apolar and slightly polar side chains are exposed to the lipid environment.

Another observation is that the end of the unfolded beta-barrel is sticking out of the membrane, and contains many charged side chains as well, while the boundary between this part and the transmembrane domain is quite apolar. Overall this structure gives the impression to be still highly stable, but perhaps less stable than the native beta-barrel, anchored in the lipid bilayer.

As this large scale conformational change should have a large effect on the behaviour of the protein, the angle between OmpA and the membrane normal was measured over time. To visualize trends in the data, a running average was calculated with a window of 100 frames. Fig 6. shows that this angle oscillates stably around 84.9 degrees. However after 10 ms of simulation, the angle suddenly shifts to 84 degrees. This could be an indication that the usual right-angle of OmpA is perhaps not so stable in the new conformation this fusion protein adopts.

Conclusions

In conclusion, it seems that the system is working as intended, as the OmpA-anti-GFP fusion protein stays anchored in the lipid bilayer and remains able to strongly bind GFP as expected. Whether this is the real situation is however impossible to know as the fusion abolishes some beta-sheets in OmpA that are important for beta-barrel formation.

Discussion

It is always difficult when modeling these kinds of processes to predict the time scale of the whole event. The current model helps us to predict that the flipping process is very slow or unfeasible at all. The latter hypothesis might be reasonable enough and it would allow us to predict that the surface display system requires additional machinery which is found in living organisms. Therefore, it is unlikely to achieve a more accurate model without extra experimental information.

In eXplaY we model a system in a pure DOPC bilayer, which is also a simplified version of natural systems. Original E. coli lipids composition can make a huge impact to the model and its’ results as well.

Potential of mean force(PMF) simulations on pulling the anti-GFP across the membrane needs to be made in order to prove that the energy barrier is really high and the process can not occur naturally. Additionally, to observe flipping in a modeled system, higher temperature (37°C) might be a promising solution.

References

1. Freudl, R. Insertion of peptides into cell-surface-exposed areas of the Escherichia coli OmpA protein does not interfere with export and membrane assembly. Gene 82, 229-236, doi:https://doi.org/10.1016/0378-1119(89)90048-6 (1989).
2. Pleckaityte, M., Mistiniene, E., Lasickiene, R., Zvirblis, G. & Zvirbliene, A. Generation of recombinant single-chain antibodies neutralizing the cytolytic activity of vaginolysin, the main virulence factor of Gardnerella vaginalis. BMC biotechnology 11, 100, doi:10.1186/1472-6750-11-100 (2011).
3. Twair, A., Al-Okla, S., Zarkawi, M. & Abbady, A. Q. Characterization of camel nanobodies specific for superfolder GFP fusion proteins. Molecular biology reports 41, 6887-6898, doi:10.1007/s11033-014-3575-x (2014).
4. Benhar, I. Biotechnological applications of phage and cell display. Biotechnology Advances 19, 1-33, doi:https://doi.org/10.1016/S0734-9750(00)00054-9 (2001).

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